me:
>> Isn't it conventional (orthodox) economics that assumes ergodicity?
>> According to Paul Davidson, who should know, it's Keynes who rejected
>> ergodicity.
Julio Huato:
> Not only [orthodox?] economists. People operating in financial markets and,
> in general, people leading a life have to do this. Keynes, in his practice
> as a speculator, had to do this as well. He assumed that "the existing state
> of affairs will continue indefinitely, except in so far as we have specific
> reasons to expect a change." ...<
Yes, _in practice_ people (including Keynes) assume ergodicity as part
of a convention. But when Keynes was doing serious theoretical
thinking (when he was examining the world as an economist rather than
participating in the world as a speculator), he did not make that
assumption (at least according to Davidson et al.)
(By the way, that wasn't Keynes' _only_ convention. He likely agreed,
for example, that when the widows and orphans are getting into the
stock market, it's time for the professonals to leave.)
Orthodox economics differs from Keynes by assuming ergodicity in their
theory, starting with an ideal and impossible world as their
base-line. Flying in the face of their scientific pretensions, these
days they don't even mention this assumption. It's part of the
ideological air they breathe, so it's taken for granted.
me:
>> Where do conventions come from? do they fall from the sky? are they innate
>> in the mind? No, they come from social practice and from nowhere else.
>> People make them. <<
[BTW, this is a paraphrase of an old chestnut from old chairperson Mao.]
> Well, what is Keynes talking about?
Keynes was mostly descriptive rather than theoretical in his
description of "where conventions come from." He studied Freud and
psychologists of the broadly-defined Freudian school (as far as I can
tell) instead of social psychology or sociology. The latter seem
necessary.
As far as I can tell, his main emphasis was how conventions allow
people to take leaps of faith in the face of deadly uncertainty and
how such unwritten rules can be destroyed. He was saying that stable
operation of markets (especially those involving the unknown future)
requires the existence of conventions, in Keynes' view, but (as far as
I know) didn't look into the interpersonal dynamics behind them.
It's like saying that the stable operation of markets requires clear
individual property rights, law and order, etc., official laws imposed
by the state. But it adds something: stable markets also require
unwritten rules of social behavior (conventions). It seems nowadays,
for example, that more and more economists see social conventions of
_trust_ as necessary to the stable operations of markets. Part of the
current financial melt-down is that this trust has evaporated, with
financiers fearing Madoffs under every bed.
If we want to understand the origins of conventions such as trust, we
have to think about relationships among people and how they evolve
over time. An incomplete story comes from game theory (the closest
most economists get to sociology) where a "game" has more than one
equilibrium. Which one is chosen (drive on the right side vs. the left
side of the road) is a matter of convention. In this case, which
convention is chosen could be random, the result of a decision by some
king centuries ago, or a democratic agreement. In most cases,
conventions are left over from the past and are slowly adapted to
current conditions (but sometimes collapse).
As far as I know, no-one has ever presented a complete theory of the
origin of conventions. (I'm not an expert on the sociological
literature.) But there's nothing wrong with thinking inductively,
bringing in the empirical _fact_ that conventions exist and pointing
to their role in (say) economics.
> Isn't the whole point to grasp the laws of social practice? <
It depends whose point Julio is talking about. Orthodox economics, for
example, is into equilibrium more than a process such as "social
practice."
> If the social practice that creates a
> convention is a process, then you model it as a process:
>
> \dot{x} = f(x, ...) or x_t = f(x_{t-k}, ...)
For those who prefer prose, that's quite opaque, especially since
Julio does not define "x." As far as I can tell, he's saying history
matters, i.e., that the nature of the situation at any specific time
(x at time t) depends on what had happened before that (x at time
{t-k} with k = 1 ... infinity).
It's unclear whether "x" is a scalar, a vector, or a matrix in this
schema. Most likely, no social convention can be quantified. How does
one quantify, for example, the convention that people drive on the
right side of the road in some countries and the left side of the road
in others? I guess one can use a quantitative method (e.g., game
theory) to help gain some understanding of that convention, but one
can't describe the actual convention mathematically.
How does one quantify "trust"? It's not like the price of tea; it's
more a matter of a psychological mood.
> Whether you are an 80-year-old historian or anthropologist with the most
> complex, refined, and subtle understanding of concrete social process, one
> way or another, with or without math, you make that sort of stipulation. ...<
I can't speak for historians or anthropologists, but one think they do
is to avoid the economists' assumption that all of us are isolated
individuals, instead looking at people as products and perhaps even
the makers of their society. Anthropologists, for one, look at the
"seamless web" of social relationships, including market institutions
are embedded to one degree or another in the broader social structure.
Historians seem less united on this issue (cf. the persistence of the
"great man" theory of history).
I agree that both groups tend to look as the past as prologue, i.e.,
seeing history as helping to determine the nature of the institutions
we live in and also what we want out of those institutions. They
wouldn't see institutions as being quantifiable.
> Similarly , if there's uncertainty about a social process, you model it as a
> stochastic process... And that is so regardless of how complicated or
> simplistic your notion of the stochastic term ... may be.<
Uncertainty is not the same as the "stochastic term" randomness. With
uncertainty (non-ergodicity), the probabilities of all the events seen
as possible do not add up to 100%. At least that's the way Davidson
explains it. People like Frank Knight and John Maynard Keynes had
other explanations.
Do people in economics grad school study people like Knight or Keynes
any more? or do people simply learn the current orthodoxy (and debates
within it)?
> Next questions are typically about how people form their expectations
> of this stochastic process, by itself or in interaction with other
> processes. E.g.:
>
> E(x_{t+k}|I_t), ...
>
> var(x_{t+k}|I_t), ...
> Cov(x_{t+k}, y_{t+k}, ...|I_t)
> ...
>
> And *that* is what I'm talking about.
I don't understand what Julio is is talking about here, since he
doesn't define either "I" or "y." Or "x" for that matter. The point of
math is to communicate in a logical way, not to shock and awe other
people. He may belong to a subsociety that attaches clear meanings to
these numbers as a matter of convention (so that definitions are
unneeded), but I don't belong to that one.
Though it's hard to tell for sure, Julio seems to follow Muth's
Mistake, to equate "expectations of the future" (subjective guesses)
with the the expected value of a variable which involves a certain
amount of well-behaved randomness. One problem is that there may be
_no_ given expected value given current information. To have an
expected value, we must not only quantify something but also assume
that there exists a well-behaved or Gaussian random distribution of
that variable (see below).
For example, we can't assume that the profit rate in the US in 2010
has a well-behaved distribution around some knowable mean. The future
is unknowable until we get there. This is especially true since our
decisions now help determine the nature of the future. (There is "path
dependence.") If businesses now expect low profits in 2010, for
example, they might cut back on investment further, worsening the
recession and actually causing the profit rate to equal zero in 2010.
Life sometimes involves self-fulfilling prophecies. (This is
especially true of financial markets, it seems.)
In mathematical terms, the statistical expected value of the future
profit rate can be a function of current business expectations of the
profit rate in the future.
me:
>> By the way, the conventions that Keynes referred to are hardly
>> complex.
Julio:
> I hope I showed that the opposite is true. How the ergodic assumption
> emerges socially is far from obvious. It needs to be explained.
Asserting that something that's complex can be quantified as "x" isn't
the same thing as showing that it's true.
We can get a preliminary understanding of the origins of the emergence
of the ergodic assumption in the society of economists. Paul Samuelson
and other engineer-economists decided that it was necessary to
economics. Because people were awed by their mathematical prowess, and
because people like him were able to claw their way to the top of the
profession, with tenure-granting power, more and more economists were
willing to think in his ergodic way. Besides, using math gives one an
upper hand in competition with older colleagues who don't know the
newest techniques. The stagnation of the alternative
(institutionalist) school after World War II likely helped with the
rise of this world-view, as did the tendency for ambitious "Young
Turks" to grab onto the newest fashion. This style of economics likely
fit with the military-industrial complex's domination of academia
after World War II. For example, the institutionalists were decimated
by the Truman-McCarthy purges. (I still haven't read Phil Mirowski's
book on the subject, alas.)
Perhaps Julio is talking about the issue of the origins of "the
ergodic assumption" in other social institutions besides the economics
profession. It would depend on which institution we're discussing.
There are no deductive rules that allow us to derive the origins of
conventions in an _a priori_ way with no further knowledge of the
institutions in question. Instead, we have to think inductively part
of the time. That is, we need to study the world rather than simply
developing nice models that purport to describe it.
There is some logic to social processes, but I can't claim to be an
expert on it. I do know that we have to go beyond thinking of the
world as (in essence) nothing but markets. The convention of trust in
financial markets, for example, might arise partly due to existence of
social clubs, where financiers get together to drink, gossip, talk
about sports, etc. (Of course, someone like Madoff can exploit such
clubbiness, but that's another story.)
>> Note, however, that the EMH is based on an unrealistic (Gaussian) view
>> of probability with no true (Knight/Keynes) uncertainty or "black
>> swans."
> What do you mean by "Gaussian" view of probability?
See Mandelbrot, THE (MIS)BEHAVIOR OF MARKETS (Basic Books, 2004),
chapter 2. He compares Gaussian probability (the randomness of games
like flipping a fair coin) with that of Cauchy (the randomness of a
blindfolded archer shooting arrows). His book is much better than that
of his arrogant acolyte Nicholas N. Taleb.
> And how is the Knight-Keynes uncertainty "more realistic"? Where's
> the substantive content of "true" uncertainty?
It's more realistic because it's based on descriptions and
understandings of the real world that exists outside of our
consciousness of it, rather than being an assumption to make
deductively derived models work well.
The substantive content is that there are more things in heaven and
earth, Horatio, than are dreamt of in your philosophy. Models
(philosophical constructs) do not -- and cannot -- describe the real
world, because they involve deliberate simplification (that's their
point). They may give us some _insight_ into the workings of the real
world, but that is not the same thing as _being_ them real world or
even an accurate picture of the real world. It's a gigantic mistake to
reify models.
More substantive substantive content: Long-Term Capital Management did
its arbitrage based on the assumption of Gaussian (ergodic)
probability, but it turned out that the world didn't work that way.
Thus the company failed, despite all the high-powered economic
"knowledge" embodied in its leaders' heads. Their ergodic assumptions
helped sink their boat (helped along by their utter arrogance).
> Where do you go after
> you find a limit to human cognition?
I can only rely on my own experience. My cognition involves inadequate
ability to remember the past. So I try to use logic as much as
possible. At the same time, I try to be humble about my understanding
of the world.
> Where do you go after you make
> the point that self-referential dynamic systems are not stable? You
> either push that boundary, get around the limit, or you don't.
Sometimes systems are unstable and sometimes they are stable. Hyman
Minsky pointed to the way in which financial markets' unregulated
workings tend to move us from the latter (stable) situation to the
former.
More generally, we have to go beyond an unhealthy attachment to
deductive logic, to see inductive logic as a necessary complement for
understanding the world.
--
Jim Devine / "Segui il tuo corso, e lascia dir le genti." (Go your own
way and let people talk.) -- Karl, paraphrasing Dante.
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